Problem: Simplify the following expression: $y = \dfrac{-12r^2 - 12r}{52r}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-12r^2 - 12r = - (2\cdot2\cdot3 \cdot r \cdot r) - (2\cdot2\cdot3 \cdot r)$ The denominator can be factored: $52r = (2\cdot2\cdot13 \cdot r)$ The greatest common factor of all the terms is $4r$ Factoring out $4r$ gives us: $y = \dfrac{(4r)(-3r - 3)}{(4r)(13)}$ Dividing both the numerator and denominator by $4r$ gives: $y = \dfrac{-3r - 3}{13}$